Modern Engineering Thermodynamics

720 CHAPTER 17: Thermodynamics of Biological Systems
EXAMPLE 17.10 (Continued )
1E−18
1E−19
1E−20
log(k d /a)
1E−21
1E−22
1E−23
1E−24
300 302 304 306 309 311 313 315
Temperature (K)
FIGURE 17.15
Example 17.10, Exercise 30.
One of the most interesting unsolved problems in evolutionary biology is that of biological aging and
development. What determines the beginning and the end of growth? Why do some cells develop into one kind
of organ and other cells into a completely different organ? Also, there is a remarkable similarity between the
following biological groups:
■
■
■
■
■
■
■
The grouping of elements to form active biochemical entities (such as amino acids).
The grouping of these entities to form macromolecules.
The grouping of macromolecules to form cells.
The grouping of cells to form living creatures
(plants and animals).
1.00
The grouping of these living creatures into
productive units (families, industries, etc.).
The grouping of these families into cultures
(or societies).
0.75
The grouping of these cultures into nations.
Recently, West, Brown, and Enquist 1 discovered a single
universal curve that describes the growth of many
diverse species. A plot of a dimensionless mass,
r = ðm/MÞ 1/4 , versus a dimensionless time variable,
τ = ðat/4M 1/4 Þ − ln ½1 − ðm 0 /MÞ 1/4 Š, for a wide variety
of species shows that growth curves for all organisms
fall on the same universal curve r = 1 – e –τ (shown as
a solid line in Figure 17.16), where a is a constant, t is
time, m 0 is the mass at birth (i.e., at t = 0), and M is
the maximum body size. Their model identifies r as
the proportion of total lifetime metabolic power used
for maintenance and other activities and provides the
basis for deriving relationships for growth rates and
the timing of life history events.
Thus, there seems to be a common phenomenological
driving force that is not only responsible for the organization
of molecular structure but is also responsible
for the organization of the cultural bonds of nations
Dimensionless mass ratio, r
0.50
0.25
Data covers shrews, rats, rabbits, pigs, cows, cod,
shrimp, salmon, guppy, robins, hens, and heron.
0 0 2 4 6 8 10
Dimensionless time, τ
FIGURE 17.16
Aplotofthedimensionlessmassratio,r = ðm/MÞ 1/4 , versus
the dimensionless time variable, τ = ðat/4M 1/4 Þ −
ln ½1 − ðm 0 /MÞ 1/4 Š, for a wide variety of species. (Source: Geoffrey
West, James Brown, and Brian Enquist, “A general model for
ontogenetic growth”. Adapted by permission from Macmillan
Publishers Ltd: Nature 413, no. 201, pp. 628–631, copyright 2001.)
1 Nature 413, (October 11, 2001), pp. 628–631.